Adding objects to an animation/0 sized object is still being rendered
To be clear I have searched for an answer for a while. And I have found out that there are quite a lot of solutions to this. Of these, however, 3 options are used the most. Here they are:
#1 Moving the object out of the camera field view (in a single frame).
This is probably the most easy solution of these 3. All you have to do is insert a keyframe where the desired object is in the camera field. Then just move on to the next frame, change the position of the object, so that it is no longer visible in the view of the camera. And on the end just add another keyframe. Voila! Here is the effect of removing/adding objects to the scene. I chose to go with this solution.

#2 Hiding the object in viewport (in a single frame).
The solution that is being used also really often. This option uses Hide in viewport option, which is available in Scene Collection. Basically add new keyframe, switch to the next frame in your animation timeline. Toggle visibility of the object off and add another keyframe. That's it.

#3 Changing material/texture during animation (in a single frame).
It works pretty much same like all the options listed above. The only difference is that you do not change location or visibility of the object, but you change material/texture of it.